设x→0时，ln(1+xk)与x+3√x等价无穷小量，求k．

设x→0时，ln(1+xk)与x+3√x等价无穷小量，求k．
【正确答案】：limx→0[ln(1+xk)/(x+3√x)] =limx→0[xk)/(x+3√x)] =limx→0[xk-1/3)/(x2/3+1)], k-1/3=0时，极限为1，故k=1/3．